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Iulia Gheorghita

Publications and source records attributed to Iulia Gheorghita.

5 recordsLinked to original sources
arXiv2022

Incidence varieties in the projectivized $k$-th Hodge bundle over curves with rational tails

Over the moduli space of pointed smooth algebraic curves, the projectivized $k$-th Hodge bundle is the space of $k$-canonical divisors. The incidence loci are defined by requiring the $k$-canonical divisors to have prescribed multiplicities at the marked points. We compute the classes of the closure of the incidence loci in the projectivized $k$-th Hodge bundle over the moduli space of curves with rational tails. The classes are expressed as a linear combination of tautological classes indexed by decorated stable graphs with coefficients enumerating appropriate weightings. As a consequence, we obtain an explicit expression for some relations in tautological rings of moduli of curves with rational tails.

math.AG↗
arXiv2021

$k$-canonical divisors through Brill-Noether special points

Inside the projectivized $k$-th Hodge bundle, we construct a collection of divisors obtained by imposing vanishing at a Brill-Noether special point. We compute the classes of the closures of such divisors in two ways, using incidence geometry and restrictions to various families, including pencils of curves on K3 surfaces and pencils of Du Val curves. We also show the extremality and rigidity of the closure of the incidence divisor consisting of smooth pointed curves together with a canonical or 2-canonical divisor passing through the marked point.

math.AG↗
arXiv2018

Effective divisors in the projectivized Hodge bundle

We compute the class of the closure of the locus of canonical divisors in the projectivization of the Hodge bundle $\mathbb{P}\overline{\mathcal{H}}_g$ over $\overline{\mathcal{M}}_g$ which have a zero at a Weierstrass point. We also show that the strata of canonical and bicanonical divisors with a double zero span extremal rays of the respective pseudoeffective cones.

math.AG↗
arXiv2015

Persistent Topology of Syntax

We study the persistent homology of the data set of syntactic parameters of the world languages. We show that, while homology generators behave erratically over the whole data set, non-trivial persistent homology appears when one restricts to specific language families. Different families exhibit different persistent homology. We focus on the cases of the Indo-European and the Niger-Congo families, for which we compare persistent homology over different cluster filtering values. We investigate the possible significance, in historical linguistic terms, of the presence of persistent generators of the first homology. In particular, we show that the persistent first homology generator we find in the Indo-European family is not due (as one might guess) to the Anglo-Norman bridge in the Indo-European phylogenetic network, but is related to the position of Ancient Greek and the Hellenic branch within the network.

cs.CL↗